This invention relates generally to a mode coupled tuning fork crystal resonator of the type used in timepieces and instruments requiring highly accurate time measurement, and more particularly, to a tuning fork resonator having a frequency-temperature characteristic represented by the fourth power term of a Taylor's expansion at the nominal operating temperature. Electronic wristwatches in the prior art have utilized a +5.degree. x-cut quartz tuning fork using the flexural mode of vibration because the resonator has a parabolic second order frequency-temperature characteristic at room temperature which is advantageous in precision of timekeeping. This type of resonator operates at a low frequency which results in low power consumption. However, the watch has a timing inaccuracy of a approximately twenty seconds a month.
In order to provide electronic wristwatches which have improved precision and long battery life in operation, mode coupled quartz crystal tuning fork resonators have been developed having a cubic frequency-temperature characteristic when operating at a low frequency and at room temperature. Such a development is described in detail in Japanese patent application Nos. 53-23903, 53-149499 and 53-149500. The latter two applications correspond to U.S. application ser. No. 42,732 filed May 29, 1979, which is incorporated herein by reference.
A mode coupled tuning fork type vibrator as described in application Ser. No. 42,732, has a frequency-temperature characteristic which can be represented mathematically as a Taylor's expansion about a room temperature of 20.degree. C. Therein, the first and second coefficients .alpha. and .beta. are made equal to zero whereby a frequency-temperature characteristic in cubic form is produced. This result is achieved by cutting the tuning fork resonator from the crystal at a preferred angle and with a selected thickness so as to provide close coupling between a flexural and a torsional mode of vibration. The frequency-temperature characteristics of such a resonator are quite good in that there is a variation of one part per million (ppm) or less over an operating temperature range of 0.degree. to 40.degree. C. With such a resonator used in an electronic wristwatch, the wristwatch operates with an extremely high timekeeping precision and the time variation is only a few seconds per year.
However, when wristwatches are used in a cold ambient condition, the precision of the wristwatch is affected to a large measure by the frequency-temperature characteristics which are present below the temperature of 0.degree. C. Where the previously developed mode coupled tuning fork vibrator, or an AT-cut resonator, having a cubic frequency-temperature characteristic is used as a standard frequency source for communication equipment, it is desirable that the frequency be unchanged in a wider range of temperatures than 0.degree. to 40.degree. C. because the equipment is seldom put into operation at temperatures equal to those of a human body. It is especially desired that standard frequency sources for communication equipment be subject to frequency variations of 3 ppm or less in a temperature range from -30.degree. C. to +60.degree. C. To meet such a requirement, a conventional AT-cut resonator relies on a voltage controlled crystal oscillator (VCXO) and a temperature compensated crystal oscillator (TCXO) to reduce frequency changes due to ambient temperature variations. These methods however are disadvantageous in that the oscillators consume increased energy, are large in size, and for these reasons are not suitable for use in small sized equipment.
What is needed is a mode coupled tuning fork crystal resonator which has good frequency-temperature characteristics over an extended operating range from -30.degree. to +60.degree. C.